$A$ conducting sphere of radius $10 \ cm$ is charged with $10 \ \mu C$. Another uncharged sphere of radius $20 \ cm$ is brought into contact with it and then separated. The ratio of the surface charge densities on the spheres will be ....... (in $: 1$)

Inside a charged hollow sphere,at any point the electric field $(E)$ and potential $(V)$ are

Consider three concentric metallic spheres $A, B$ and $C$ of radii $a, b, c$ respectively,where $a < b < c$. $A$ and $B$ are connected,whereas $C$ is grounded. The potential of the middle sphere $B$ is raised to $V$. Then the charge on the sphere $C$ is

$(a)$ $A$ conductor $A$ with a cavity as shown in Figure $(a)$ is given a charge $Q$. Show that the entire charge must appear on the outer surface of the conductor.
$(b)$ Another conductor $B$ with charge $q$ is inserted into the cavity keeping $B$ insulated from $A$. Show that the total charge on the outside surface of $A$ is $Q+q$ [Figure $(b)$].
$(c)$ $A$ sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.

$A$ conducting sphere of radius $10\, cm$ is charged with $10\,\mu C$. Another uncharged sphere of radius $20\, cm$ is allowed to touch it for some time. After the spheres are separated,the ratio of the surface charge densities on the spheres will be:

$A$ solid spherical conducting shell has inner radius $a$ and outer radius $2a$. At the center of the shell, a point charge $+Q$ is located. What must the charge of the shell be in order for the charge density on the inner and outer surfaces of the shell to be exactly equal?